The User Profile Synchronization service does not start on a stand-alone installation of SharePoint Server 2010

If you are trying to start User Profile Synchronization (UPS) service on a stand-alone SharePoint Server 2010 you should know that UPS is not designed to work on a stand-alone SharePoint Server 2010. Stand-alone installation means you are running SharePoint in a single-server environment.

The following KB article has more details: 983061. To configure UPS on SharePoint Server 2010 check out this article on Microsoft TechNet.